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Affine recourse for the robust network design problem: between static and dynamic routing

Please always quote using this URN: urn:nbn:de:0297-zib-12122
  • Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. We apply them to robust network design with polyhedral demand uncertainty, introducing the affine routing principle. We compare the affine routing to the well-studied static and dynamic routing schemes for robust network design. All three schemes are embedded into the general framework of two-stage network design with recourse. It is shown that affine routing can be seen as a generalization of the widely used static routing still being tractable and providing cheaper solutions. We investigate properties on the demand polytope under which affine routings reduce to static routings and also develop conditions on the uncertainty set leading to dynamic routings being affine. We show however that affine routings suffer from the drawback that (even totally) dominated demand vectors are not necessarily supported by affine solutions. Uncertainty sets have to be designed accordingly. Finally, we present computational results on networks from SNDlib. We conclude that for these instances the optimal solutions based on affine routings tend to be as cheap as optimal network designs for dynamic routings. In this respect the affine routing principle can be used to approximate the cost for two-stage solutions with free recourse which are hard to compute.

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Metadaten
Author:Michael Poss, Christian Raack
Document Type:ZIB-Report
Tag:affine adjustable robust counterparts; affine routing; network design; recourse; robust optimization
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B15 Network models, stochastic
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B18 Communication networks [See also 68M10, 94A05]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C27 Combinatorial optimization
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C90 Applications of mathematical programming
Date of first Publication:2011/02/07
Series (Serial Number):ZIB-Report (11-03)
ZIB-Reportnumber:11-03
Published in:Appeared in: Networks 61/2 (2013) pp. 180-198
DOI:https://doi.org/10.1002/net.21482
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